Question

3.5 The block diagram of an autopilot designed to maintain the pitch attitude $\theta$ of an aircraft is shown below. The transfer function relating the elevator angle $\delta_e$ and the pitch attitude $\theta$ is $\frac{\theta(s)}{\delta_e(s)} = G(s) = \frac{50(s+1)(s+2)}{(s^2+5s+40)(s^2+0.03s+0.06)}$, where $\theta$ is the pitch attitude in degrees and $\delta_e$ is the elevator angle in degrees. The autopilot controller uses the pitch attitude error $e$ to adjust the elevator according to the transfer function $\frac{\delta_e(s)}{E(s)} = D(s) = \frac{K(s+3)}{s+10}$. Using MATLAB, find a value of K that will provide an overshoot of less than 10% and a rise time faster than 0.5 sec for a unit-step change in $\theta_r$.

          3.5
The block diagram of an autopilot designed to maintain the pitch attitude $\theta$ of an aircraft is shown below.
The transfer function relating the elevator angle $\delta_e$ and the pitch attitude $\theta$ is
$\frac{\theta(s)}{\delta_e(s)} = G(s) = \frac{50(s+1)(s+2)}{(s^2+5s+40)(s^2+0.03s+0.06)}$,
where $\theta$ is the pitch attitude in degrees and $\delta_e$ is the elevator angle in degrees. The autopilot controller
uses the pitch attitude error $e$ to adjust the elevator according to the transfer function
$\frac{\delta_e(s)}{E(s)} = D(s) = \frac{K(s+3)}{s+10}$.
Using MATLAB, find a value of K that will provide an overshoot of less than 10% and a rise time faster
than 0.5 sec for a unit-step change in $\theta_r$.

3.5
The block diagram of an autopilot designed to maintain the pitch attitude θ of an aircraft is shown below.
The transfer function relating the elevator angle and the pitch attitude θ is
(θ(s))/((s)) = G(s) = (50(s+1)(s+2))/((s^2+5s+40)(s^2+0.03s+0.06)),
where θ is the pitch attitude in degrees and is the elevator angle in degrees. The autopilot controller
uses the pitch attitude error e to adjust the elevator according to the transfer function
((s))/(E(s)) = D(s) = (K(s+3))/(s+10).
Using MATLAB, find a value of K that will provide an overshoot of less than 10% and a rise time faster
than 0.5 sec for a unit-step change in .

Added by Ricardo H.

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